In this context, in Section , we show that \(T(X_1^n)\)  is suitable to estimate the mean in high dimension in a heavy-tailed and corrupted setting. In the literature, there are estimators that have strong theoretical guarantees but that are intractable, for example one can see estimators based on the aggregation of one-dimensional estimators (same idea as projection pursuits), see [1]} and reference therein, see also [2]} and there has also been estimators based on depth, for example Tukey's median [3]}. On the other hand, there are tractable algorithms but whose theoretical guarantees are lacking for example the coordinate-wise median or the geometrical median [4]}, [5]}, our work belong to this type of methods, our estimator is easily computable and even though the obtained error bounds are much better than for the coordinate-wise median, at least in corrupted setting it is not minimax. Recently there have been several propositions of algorithms whose goal was to be at the same time tractable and minimax, see [6]}, [7]}, [8]}, [9]} however these algorithms are often hard to implement and in practice the complexity makes them intractable for high-dimensional problems.
